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Lecture 20 Instrumental variable estimation

# Lecture 20 Instrumental variable estimation - Economics 326...

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Economics 326 Methods of Empirical Research in Economics Lecture 20: Instrumental variable estimation Vadim Marmer University of British Columbia May 5, 2010

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Endogeneity I In the linear regression model, Y i = β 0 + β 1 X i + U i the condition for consistent estimation of β 1 by OLS is that X is exogenous: Cov ( X i , U i ) = 0 . I When Cov ( X i , U i ) 6 = 0 , we say that the regressor X in endogenous. I When the regressor is endogenous, the OLS estimator is inconsistent: ˆ β 1 , n β 1 = 1 n n i = 1 ( X i ¯ X n ) U i 1 n n i = 1 ( X i ¯ X n ) 2 ! p Cov ( X i , U i ) Var ( X i ) 6 = 0 . 1/18
Consequences of endogeneity I The causal e/ect of X on Y is not estimated consistently: ˆ β 1 , n ! p β 1 + Cov ( X i , U i ) Var ( X i ) . The e/ect can be over or under estimated depending on the sign of Cov ( X i , U i ) . I 2±18

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Sources of endogeneity There are several possible sources of endogeneity: 1. Omitted explanatory variables. 2. Simultaneity. 3. Errors in variables. All result in regressors correlated with the errors. 3/18
Omitted explanatory variables I Suppose that the true model is ln Wage i = β 0 + β 1 Education i + β 2 Ability i + V i , where V i is uncorrelated with Education and Ability . I Since Ability is unobservable, the econometrician regresses ln Wage against Education , and β 2 Ability "goes" into the error part: ln Wage i = β 0 + β 1 Education i + U i , U i = β 2 Ability i + V i . I Education is correlated with Ability : we can expect that Cov ( Education i , Ability i ) > 0 , β 2 > 0, and therefore Cov ( Education i , U i ) > 0 . Thus, OLS will overestimate the return to education. 4/18

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Simultaneity I Consider the following demand-supply system: Demand: Q d = β d 0 + β d 1 P + U d , Supply: Q s = β s 0 + β s 1 P + U s , where: Q d = quantity demanded, Q s = quantity supplied, P =price. I
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Lecture 20 Instrumental variable estimation - Economics 326...

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